It doesn't consist of the same photons; the spot in the "new" position consists of photons which have been traveling in a straight line from your flash light at (assuming vacuum) a constant rate of C (and then reflected back to reach your eye again, also at a constant rate of C); they haven't traveled to or from the previous "spot" position at all, much less exceeded the speed of light at any point in the process of reaching the new position.
Right?
AFAIK Expansion of the universe is comparable. It pushes things away not by speed but by putting extra 'new' space between things.
Your sibling comment makes a variant of the same point:c is the maximal speed of information or causality. Light in a vacuum is just one of the things capable of reaching it.
And what you point out is actually the speed limit of causality, instead of light. It just happens that light travel really fast.
Though the article wants to discuss the speed of light as you mentioned, so I focused on speed of light.
As a standard example, take a wall at 1m distance and a flashlight. move the light spot at 1 m/s. If you put the wall at 2m, the same spot will now go 2 m/s. If you put it at 300 000 km, the spot will go at 300 000 km/s, slightly over light speed.
The problem is more one of information: For any action you take, no consequence can happen outside your light cone. All information you generate travels at c at max.
None of the examples you gave violates this: Even if the universe expands at more than c, nothing you do will have influence on things too far from you.